CN113189979A - Distributed queue finite time control method of unmanned ship - Google Patents

Distributed queue finite time control method of unmanned ship Download PDF

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CN113189979A
CN113189979A CN202110363566.0A CN202110363566A CN113189979A CN 113189979 A CN113189979 A CN 113189979A CN 202110363566 A CN202110363566 A CN 202110363566A CN 113189979 A CN113189979 A CN 113189979A
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unmanned ship
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CN113189979B (en
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梁晓玲
王端松
王川
朱鹏莅
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Dalian Maritime University
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Abstract

The invention discloses a distributed queue type finite time control method of an unmanned ship, belonging to the distributed queue type finite time control method of the unmanned ship, comprising the following steps: establishing a formation kinematics and dynamics model of the unmanned ship; the method comprises the following steps of defining the relative position and angle between unmanned ship formation by adopting a line-of-sight strategy, and meeting the constraint conditions of the minimum collision avoidance distance and the maximum effective communication distance between a piloting unmanned ship and a following unmanned ship by utilizing the barrier Lyapunov function design; designing a virtual control law according to error information obtained by the expected position and heading information; based on a virtual control law, a neural network adaptive control, a disturbance observer and a full-state feedback full-drive unmanned ship design output constraint formation controller, distributed formation type finite time control of the unmanned ship is realized, and stability proves that formation errors of the full-drive unmanned ship can be converged into any small neighborhood near zero in finite time.

Description

Distributed queue finite time control method of unmanned ship
Technical Field
The invention relates to the field of unmanned ship formation, in particular to a distributed queue finite time control method for an unmanned ship.
Background
When the unmanned ship formation system runs from a wide sea area to a narrow sea area, the formation needs to be switched, the tracking performance of a pilot needs to be considered, and the formation error between the pilot and a follower cannot be too large. In the queue switching process, when the distance between two ships is too large, the communication range of the sensor is exceeded, and the problem of communication failure or channel collision is caused; when the distance between the two ships is too small, it will be less than the safe distance between the ships, and the risk of collision between the ship bodies is easily generated. At present, aiming at unmanned ship formation control, most of the unmanned ship formation control only considers whether a formation system can finally reach an expected formation, and does not consider the constraint problem of formation errors. The preset performance function and the barrier Lyapunov function can effectively solve the problem of error constraint in the control process, and have been used for ship path tracking control, robot control and unmanned aerial vehicle control. Some learners use a preset performance function to constrain the distance and angle errors of a line-of-sight method within an expected range through coordinate conversion, so that the problem of transient performance constraint in the row-type formation process of the fully-driven unmanned surface vessel is solved, but the design of a controller is complicated. For the research of output constraint in ship control, the logarithm barrier Lyapunov function is a research hotspot, and is applied to the trajectory tracking control of the fully-driven unmanned ship, so that the problem of symmetric output constraint is solved; at present, most of researches on the output constraint of ship motion control are constraint control of a single system, and the research result on the output constraint of ship formation control is still less.
Research on finite time control of ships has still largely focused on single-ship control research. Early scholars studied the problems of perturbation of model parameters and trajectory tracking control of under-actuated unmanned underwater vehicles under constant unknown ocean currents. A kinematics controller is designed by adopting an equivalent control method of proportional-integral-derivative sliding mode control. And thirdly, two dynamic controllers are respectively designed by utilizing the first-order sliding mode surface and the second-order sliding mode surface, so that the global convergence of all tracking errors in limited time is ensured. The subsequent research aims at input saturation and unknown interference, the finite time trajectory tracking control of the unmanned ship is researched by adopting integral sliding mode control and a homogeneous disturbance observer, the input saturation nonlinearity is adaptively approximated by using a smooth function, and the total uncertainty can be accurately estimated in a short time by constructing the homogeneous disturbance observer. Theoretical analysis shows that the whole closed-loop tracking system is globally stable in limited time, and simulation research proves the effectiveness and superiority of the method. The track tracking of the fully-driven ship underwater vehicle under the condition of model uncertainty and external interference is researched based on a second-order fast terminal sliding mode, and the designed second-order sliding mode surface can realize fast convergence and avoid the occurrence of singular values. Elmokadem considers the transverse motion control of an under-actuated underwater vehicle under nonlinear dynamics, unmodeled dynamics, system uncertainty and external environment interference, realizes track tracking control by using two methods of terminal sliding mode control and rapid terminal sliding mode control, and can ensure the convergence of the system in limited time but have the problem of singular value; in order to mitigate the effects of environmental interference and model uncertainty, their upper bounds need to be known, which is difficult to obtain in practice. In addition, the controllers are designed for a single ship, and most of the control methods for the mono-hull system cannot be directly applied to the research of the multi-hull system due to the complexity of the formation control system.
Disclosure of Invention
According to the problems existing in the prior art, the invention discloses a distributed queue limited time control method of an unmanned ship, which comprises the following steps:
establishing a formation kinematics and dynamics model of the unmanned ship;
based on kinematics and dynamics models of unmanned ship formation, the relative position and angle between unmanned ship formations are defined by adopting a strategy of a line-of-sight method, and constraint conditions of minimum collision avoidance distance and maximum effective communication distance between a piloting unmanned ship and a following unmanned ship are met by utilizing barrier Lyapunov function design;
on the basis of a kinematic and dynamic model, obtaining the relative position and angle between a piloting unmanned ship and a following unmanned ship of an unmanned ship formation, and designing a virtual control law according to error information obtained by expected position and heading information under the constraint conditions of meeting the minimum collision avoidance distance and the maximum effective communication distance between the piloting unmanned ship and the following unmanned ship;
based on an uncertain item in the dynamic model, adopting a radial basis function neural network to design compensation feedback control;
estimating unknown marine environment interference in a dynamic model, and designing a disturbance observer;
based on a virtual control law, a neural network self-adaptive control, a disturbance observer and a full-drive unmanned ship with full-state feedback, the output constraint formation controller is used for realizing the distributed queue finite time control of the unmanned ship.
Further, the disturbance of the marine environment is estimated, and an expression of a disturbance observer is designed as follows:
Figure BDA0003006503090000021
wherein: miRepresenting the system inertia matrix, CiRepresenting the Coriolis centripetal force matrix, tauiRepresents a control input, HiIs that the Gaussian function is a Gaussian function, z2iWhich is indicative of a velocity vector tracking error,
Figure BDA0003006503090000022
representing the disturbance estimate, xi is the disturbance estimate intermediate design variable, alphai＝[α1i,α2i,α3i]TRepresenting the virtual control rate.
Further, the expression of the output constraint formation controller is as follows:
Figure BDA0003006503090000031
wherein
Figure BDA0003006503090000032
(·)+Represents the generalized inverse of (·),k1i,k2i,k3i,k4iis a design parameter, kai、kbiIs the line of sight angle e between two vesselsψiAnd a distance ediAnd (4) limiting.
Due to the adoption of the technical scheme, the distributed queue finite time control method of the unmanned ship, provided by the invention, for a fully-driven unmanned ship formation system, the barrier Lyapunov function is adopted to ensure that a leader and a follower are in a safe distance and in a communication connection range, then under the condition of multiple constraints of immeasurable speed, model uncertainty and external interference, a radial basis function neural network is used for approaching the model uncertainty, an interference observer designed based on the foregoing estimates the external environment interference, a full-state feedback robust finite time formation controller under the multiple constraints is provided, and the formation state error of the fully-driven unmanned ship can be converged to any small neighborhood near zero within finite time.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a diagram of formation plots in a northeast coordinate system;
FIG. 2 is a graph of the velocity of each vessel;
FIG. 3 is a graph of control inputs for each of the vessels;
FIG. 4 is a graph of a formation distance error;
FIG. 5 is a graph of the formation angle error;
FIG. 6 is a graph of environmental interference observation error values.
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following describes the technical solutions in the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention:
a distributed queue finite time control method of an unmanned ship comprises the following steps:
s1, establishing a formation kinematics and dynamics model of the unmanned ship;
s2, based on kinematics and dynamics models of unmanned ship formation, adopting a strategy of a line of sight method to define relative positions and angles between unmanned ship formations, and utilizing barrier Lyapunov function design to meet constraint conditions of minimum collision prevention distance and maximum effective communication distance between a piloted unmanned ship and a following unmanned ship;
s3, obtaining the relative position and angle between the piloting unmanned ship and the following unmanned ship of the unmanned ship formation on the basis of the kinematics and dynamics model, and designing a virtual control law according to the error information obtained by the expected position and heading information under the constraint conditions of meeting the minimum collision avoidance distance and the maximum effective communication distance between the piloter unmanned ship and the following unmanned ship;
s4, designing and compensating feedback control by adopting a radial basis function neural network based on the uncertain item in the dynamic model;
s5, aiming at unknown environmental interference in the dynamic model, designing a disturbance observer to estimate the marine environmental disturbance;
and S6, realizing distributed queue type finite time control of the unmanned ship based on a virtual control law, a neural network self-adaptive control, a disturbance observer and a full-state feedback full-drive unmanned ship output constraint formation controller.
The steps S3, S4, and S5 may be executed in parallel;
further, the process of establishing the unmanned ship formation kinematics and dynamics model is as follows:
considering a formation system (numbered 0,1, … N) containing N +1 unmanned vessels, the kinematic model of the ith fully driven unmanned surface vessel can be expressed as:
Figure BDA0003006503090000041
the kinetic model can be expressed as:
Figure BDA0003006503090000042
wherein eta isi＝[xi,yi,ψi]TIs a position state vector, x, of the unmanned ship in a northeast coordinate systemiRepresenting the north position, y, of the hull in an inertial frameiShowing the east position of the hull in an inertial frame, psiiRepresenting the heading angle, ui＝[ui,νi,ri]TIs a velocity vector u in a hull coordinate systemiRepresenting the longitudinal speed, v, of the hulliIndicates the speed of horizontal drift, riIndicating yaw rate, taui∈R3×1Representing a control input, di∈R3×1For containing forces generated by external environmental disturbances, Mi∈R3×3Representing the inertia matrix, C, of the surface vessel systemi(υi)∈R3×3Representing the Coriolis centripetal force matrix, Ri(υi)∈R3×3For surface vessel system fluid damping matrices, Ji(ψi)∈R3×3A transformation matrix is represented that is,
Figure BDA0003006503090000043
further, on the basis of kinematic and dynamic models, defining relative positions and angles between unmanned ship formations based on a strategy of a line of sight method;
relative distance rho between piloted unmanned ship and following unmanned shipiIs defined as:
Figure BDA0003006503090000051
relative angle
Figure BDA0003006503090000052
Comprises the following steps:
Figure BDA0003006503090000053
considering collision avoidance and communication distance constraints, a formation error is defined as:
Figure BDA0003006503090000058
wherein: e.g. of the typediThe relative distance error between the piloter and the follower of the unmanned ship is represented by rhoiRepresenting the desired relative distance between the pilot and the follower of the unmanned ship by ρi,desIs represented by eψiIndicating the relative heading angle error, psi, between the drone navigator and the followeriIndicating the heading angle, psi, between the followers of the unmanned shipi-1Indicating the unmanned ship pilot heading angle.
The following conditions (minimum collision avoidance distance and maximum effective communication distance constraint conditions) are strictly satisfied in the whole queue movement process:
Figure BDA0003006503090000054
wherein: ,
Figure BDA0003006503090000055
in order to satisfy the constraint condition of the maximum effective communication distance,e diis the minimum collision avoidance distance constraint condition;
Figure BDA0003006503090000056
for the maximum line-of-sight angle constraint in effective communications,e ψiis the constraint condition of the collision avoidance distance and the sight angle.
The tracking error for defining the position vector and the velocity vector is as follows
z1i＝[z11i,z12i]T＝[edi,eψi]T
z2i＝[z21i,z22i,z23i]T＝vi-αi (12)
Wherein: z is a radical of1iFor position vector tracking errors, z11iIs the relative distance error between the pilot and the follower, z12iFor the relative heading angle error between the pilot and the follower, z2iFor velocity vector tracking errors, z21iFor longitudinal velocity tracking error, z22iFor transverse velocity tracking error, z23iThe deviation angular velocity tracking error.
Further, a virtual control law alpha is designed according to the expected position and heading information of the unmanned shipi＝[α1i,α2i,α3i]TWherein:
Figure BDA0003006503090000057
wherein: alpha is alphaiAs virtual control law vectors, α1iFor the relative position virtual sub-control law, alpha2iFor a relative line-of-sight angle virtual sub-control law, alpha3iIs a virtual control law of the heading angle, kdiDesign parameters for location, kψiDesign parameters for angle, ediFor the relative distance error between the pilot and the follower of the unmanned ship, eψiThe relative heading angle error between the piloter and the follower of the unmanned ship.
Further, based on the radial basis function neural network approximation uncertainty, designing compensation feedback control;
due to the damping matrix Ri(υi) The uncertain part causes that the model-based control algorithm cannot be realized in practice or the system control precision cannot be ensured, so that most of the model-based control algorithms are infeasible, and the neural network technology is used for damping matrix Ri(υi) The uncertain part is estimated to improve the performance of the control system;
Wi *THi(Zi)+εi(Zi)＝-Ri(υi)υi. (14)
use function
Figure BDA0003006503090000061
Approaches to the ideal value Wi *THi(Zi)，
Figure BDA0003006503090000062
Is the estimated weight of the radial basis function neural network.
The self-adaptive updating law design of the neural network comprises the following steps:
Figure BDA0003006503090000063
wherein the content of the first and second substances,
Figure BDA0003006503090000064
is an adaptive gain matrix, σiIs a normal number, Hi(Zi) Is a Gaussian function, ZiIs the input value of a gaussian function;
differentiating the state error on both sides can obtain:
Figure BDA0003006503090000065
wherein Di＝εi(Zi)+di，
Aiming at unknown environmental interference in the dynamic model, designing a disturbance observer to estimate the marine environmental disturbance;
Figure BDA0003006503090000066
wherein: miRepresenting the system inertia matrix, CiRepresenting the Coriolis centripetal force matrix, tauiRepresents a control input, HiIs a Gaussian function, z2iWhich is indicative of a velocity vector tracking error,
Figure BDA0003006503090000067
representing the disturbance estimate, xi is the disturbance estimate intermediate design variable, alphai＝[α1i,α2i,α3i]TIs the designed virtual control rate.
Further, a full-drive unmanned ship self-adaptive neural network output constraint formation controller based on full-state feedback is designed as follows:
Figure BDA0003006503090000068
wherein
Figure BDA0003006503090000069
(·)+Represents the generalized inverse of (·), k1i,k2i,k3i,k4iIs a design parameter, kai、kbiIs the line of sight angle e between two vesselsψiAnd a distance ediThe boundary is defined by the distance between the two ends,
Figure BDA0003006503090000071
further, the stability of the system design is demonstrated considering the following lyapunov function:
Figure BDA0003006503090000072
wherein the content of the first and second substances,
Figure BDA0003006503090000073
is the estimation error of the network weight, V2iIs the Lyapunov function, MiFor tracking error parameter matrix, z2iIn order for the velocity to track the error vector,
Figure BDA0003006503090000074
for the estimation error of the network weight values,
Figure BDA0003006503090000075
is a disturbance error;
lyapunov function V2iThe time derivative of (d) can be calculated as:
Figure BDA0003006503090000076
Figure BDA0003006503090000077
Figure BDA0003006503090000078
Figure BDA0003006503090000079
wherein: kappa0iControlling the gain, κ, for the Lyapunov function1iControlling the gain, V, in a fractional order for the Lyapunov function2iIs the Lyapunov function, oiTo converge domain, k1iControlling gain, k, for relative distance2iFor controlling gain, k, relative to line-of-sight angle3iControlling gain, k, for velocity vectors4iControlling the gain, σ, for a fractional order of the velocity vectoriAnd (3) self-adaptive design parameters of the neural network, wherein l is a finite time fractional order design parameter.
Adjustment of κ0i，κ1iAnd then the system error state converges to a balance point within a limited time, further, the limited time queue advancing of the fully-driven unmanned ship under the conditions of model uncertainty and unknown environmental interference can be obtained, and the constraint conditions of the minimum collision avoidance distance and the maximum effective communication distance are met.
Verifying the effectiveness of the provided self-adaptive neural network output constraint formation control method of the fully-driven unmanned ship through simulation; the trajectory of the pilot is set to the form:
Figure BDA00030065030900000710
the initial state information for each ship is as follows: eta0＝[0，0，0]T，η1＝[0，5，0]T，η2＝[0，10，0]T，η3＝[0，15，0]T，ui＝νi＝r i0. For a neural network approximation function, the selected input is Z1i＝ui，Z2i＝Z3i＝[vi,ri]，
Figure BDA00030065030900000711
Using 27 nodes, the center point values are distributed over the interval [0,1.2 ]]The width of the Gaussian base function is set to 0.1,
Figure BDA00030065030900000712
using 49 nodes, the central value is distributed in the interval [ -0.9,0.1 [)]×[2,2]The width of the Gaussian base function is set to 0.1,
Figure BDA0003006503090000081
using 49 nodes, the central value is distributed in the interval [ -1,0.2 [ ]]×[2,2]The width of the gaussian base function is set to 0.2.
FIG. 1 is a diagram of formation plots in a northeast coordinate system; FIG. 2 is a graph of the velocity of each vessel; FIG. 3 is a graph of control inputs for each of the vessels; FIG. 4 is a graph of a formation distance error; FIG. 5 is a graph of the formation angle error; both the distance error and the angle error can eventually converge to a smaller neighborhood around zero, and the errors are always within the constraints throughout the formation process. The distance between each ship is larger than the minimum collision avoidance distance and smaller than the maximum communication distance, and the effectiveness of the barrier Lyapunov function technology is proved; in addition, the error of the follower 1 is obviously smaller than that of other followers, because the follower 1 can directly obtain information from the pilot, and the followers 2 and 3 need to pass through more transmission chains to obtain information, so that the error is higher, and the formation error is finally still converged into a small range of the origin; fig. 6 is an environmental interference observation error value diagram showing an observation error of an interference observer with respect to an external time-varying environmental interference value, and the observation error value can be converged to a small neighborhood near the origin through adjustment in an initial process, thereby proving the validity of the proposed observer.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (3)

1. A distributed queue finite time control method of an unmanned ship is characterized by comprising the following steps: the method comprises the following steps:
establishing a formation kinematics and dynamics model of the unmanned ship;
based on kinematics and dynamics models of unmanned ship formation, the relative position and angle between unmanned ship formations are defined by adopting a strategy of a line-of-sight method, and constraint conditions of minimum collision avoidance distance and maximum effective communication distance between a piloting unmanned ship and a following unmanned ship are met by utilizing barrier Lyapunov function design;
on the basis of a kinematic and dynamic model, obtaining the relative position and angle between a piloting unmanned ship and a following unmanned ship of an unmanned ship formation, and designing a virtual control law according to error information obtained by expected position and heading information under the constraint conditions of meeting the minimum collision avoidance distance and the maximum effective communication distance between the piloting unmanned ship and the following unmanned ship;
based on an uncertain item in the dynamic model, adopting a radial basis function neural network to design compensation feedback control;
aiming at unknown marine environment interference in a dynamic model, designing a disturbance estimation observer;
based on a virtual control law, a neural network adaptive control, a disturbance observer and a full-state feedback full-drive unmanned ship design output constraint formation controller, the distributed formation type finite time control of the unmanned ship is realized.
2. The method of claim 1, further characterized by: the expression of the disturbance observer estimation according to the marine environment disturbance is as follows:
Figure FDA0003006503080000011
wherein: miRepresenting the system inertia matrix, CiRepresenting the Coriolis centripetal force matrix, tauiRepresents a control input, HiIs a Gaussian function, z2iWhich is indicative of a velocity vector tracking error,
Figure FDA0003006503080000012
representing disturbance estimate, ξ -disturbance estimate intermediate design variable, αi＝[α1i,α2i,α3i]TA virtual control rate.
3. The method of claim 1, further characterized by: the expression of the output constraint formation controller is as follows:
Figure FDA0003006503080000021
wherein
Figure FDA0003006503080000022
(·)+Represents the generalized inverse of (·), k1i,k2i,k3i,k4iIs a design parameter, kai、kbiIs the line-of-sight angle error e between two vesselsψiAnd a distance error ediAnd (4) limiting.
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